The rectangular assignment problem is a generalization of the linear assignment problem (LAP): one wants to assign a number
of persons to a smaller number of jobs, minimizing the total corresponding costs. Applications are, e.g., in the fields of
object recognition and scheduling. Further, we show how it can be used to solve variants of the LAP, such as the k-cardinality
LAP and the LAP with outsourcing by transformation. We introduce a transformation to solve the machine replacement LAP.We
describe improvements of a LAP-algorithm for the rectangular problem, in general and slightly adapted for these variants,
based on the structure of the corresponding cost matrices. For these problem instances, we compared the best special codes
from literature to our codes, which are more general and easier to implement. The improvements lead to more efficient and
robust codes, making them competitive on all problem instances and often showing much shorter computing times.

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